Recently, by utilizing the degree sequences and the closure concept,
Liu et al. [1]} generalized Theorem REF  to
\(k\) -Hamiltonian graphs.
Clearly, the graph \(H_{n,k,\delta }= K_\delta \vee ( K_{n-2\delta +k} \cup I_{\delta -k})\)  is not
\(k\) -Hamiltonian and
\(\lambda (H_{n,k,\delta }) > n-\delta +k -1\) .
By a careful modification in ,
the correct result should be the following theorem.
